Question

Derive velocity position equation of motion graphically

Answer 1

Equation for position velocity relation

consider graph given in figure .

We know that distance travelled s by a body in time t is given by the area under line AB which is area of trapezium OABC.

So we have

Distance travelled=s= Area of Trapezium OABC

S=(sum of parallel sides) x height/2

=(OA+CB)x OC/2

since OA+CB=u+v and OC=t,

Then we gt

s=(u+v)t/2get,-------------(1)

from, velocity time relation,

t=v-u/a

substituting the value of 't' in equation 1

we get,

s=(u+v)/2(v-u)/2

or we have

v²=u²+2as

which is equation for position velocity relation